Divide the polynomials.
Answer: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice the numerator is missing a $1^{\text{st}}$ degree term. Let's add it as $0x$. $\begin{array}{r} x+1 \\ x-1|\overline{x^2+0x+2} \\ \mathllap{-(}\underline{x^2-\phantom{0}x\phantom{+2}\rlap )} \\ x+2 \\ \mathllap{-(}\underline{x-1\rlap )} \\ 3 \end{array}$ We get that the quotient is $x+1$ and the remainder is $3$, and therefore: $\dfrac{x^2+2}{x-1}=x+1+\dfrac{3}{x-1}$ [I want to see a different way of performing the division.]